Generation of a nonlinear stark shift through the adiabatic elimination method

Taking a three-level trapped atom, a Hamiltoninan with multiphonon process is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, an effective Hamiltonian for a two-level atom with a nonlinear Stark shift is obtained. Some statistical aspects for this effective Hamiltonian are presented. The temporal evolution of the atomic inversion, entropy, phase distribution and Q-function is investigated. These aspects are sensitive to the changes due to the Stark shifts. The results show that the effect of Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.